1981 The Burke & Shaw system

The Burke & Shaw system has been derived by Bill Burke and Robert Shaw from the Lorenz equations [1] The set of ordinary differential equations is

where and are the parameters. This system is invariant under a rotation symmetry around the -axis. For , a chaotic attractor is obtained (Fig. 1).

Fig. 1: Chaotic attractor

This system is a companion to the Lorenz system, in the sense that it belongs to the same class of systems. The main departure between the Burke & Shaw system and the Lorenz system is not in their equations but in the way they are organized around the axis [2]. This attractor is characterized by a four branch template (Fig. 2) [3].